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What is the Least Common Multiple of 65680 and 65690?

Least common multiple or lowest common denominator (lcd) can be calculated in two way; with the LCM formula calculation of greatest common factor (GCF), or multiplying the prime factors with the highest exponent factor.

Least common multiple (LCM) of 65680 and 65690 is 431451920.

LCM(65680,65690) = 431451920

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Least Common Multiple of 65680 and 65690 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 65680 and 65690, than apply into the LCM equation.

GCF(65680,65690) = 10
LCM(65680,65690) = ( 65680 × 65690) / 10
LCM(65680,65690) = 4314519200 / 10
LCM(65680,65690) = 431451920

Least Common Multiple (LCM) of 65680 and 65690 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 65680 and 65690. First we will calculate the prime factors of 65680 and 65690.

Prime Factorization of 65680

Prime factors of 65680 are 2, 5, 821. Prime factorization of 65680 in exponential form is:

65680 = 24 × 51 × 8211

Prime Factorization of 65690

Prime factors of 65690 are 2, 5, 6569. Prime factorization of 65690 in exponential form is:

65690 = 21 × 51 × 65691

Now multiplying the highest exponent prime factors to calculate the LCM of 65680 and 65690.

LCM(65680,65690) = 24 × 51 × 8211 × 65691
LCM(65680,65690) = 431451920